{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NONRAD Tutorial\n",
    "\n",
    "This notebook serves as a tutorial for how to use the NONRAD code to compute the nonradiative capture coefficient for a given defect. In this tutorial, we will examine the capture of a hole by the negatively charge C substiution on the N site in wurtzite GaN.\n",
    "\n",
    "\n",
    "**Recommendation**: For every function provided by NONRAD, read the docstring to understand how the function behaves. This can be done using `function?` in a notebook or `print(function.__doc__)`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. First-Principles Defect Calculation\n",
    "\n",
    "Before we begin using the code provided by NONRAD, we must perform a first-principles calculation to obtain the equilibrium structures and thermodynamic level for our defect. This results in a formation energy plot such as the following."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "Efermi = np.linspace(0., 3.5, 10)\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.plot(Efermi, - Efermi + 1.058)\n",
    "ax.plot(Efermi, np.zeros(10))\n",
    "ax.scatter(1.058, 0., color='r', marker='|', zorder=10)\n",
    "ax.text(1.058, 0., '$\\epsilon (0/-)$ = 1.058 eV', color='r', va='bottom')\n",
    "ax.set_xlabel(r'$E_{\\rm{Fermi}}$ [eV]')\n",
    "ax.set_ylabel(r'$E_f - E_f(q=0)$ [eV]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The formation energy plot tells us the most stable charge state as a function of the Fermi level. The blue line corresponds to the C substitution being in the negative charge state, and the orange line corresponds to the neutral charge state. The thermodynamic transition level is the crossing between these two lines and for this defect, we find a value of 1.058 eV. This will be one input parameter to the calculation of the nonradiative capture coefficient, `dE`. Let's save this value for later:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dE = 1.058 # eV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Compute Configuration Coordinate Diagram\n",
    "\n",
    "#### Preparing the CCD Calculations\n",
    "We now are ready to prepare our configuration coordinate diagram. The configuration coordinate diagram gives us a practical method to depict the coupling between electron and phonon degrees of freedom. The potential energy surface in each charge state is plotted as a function of displacement. The displacement is generated by a linear interpolation between the ground and excited configurations and also corresponds to the special phonon mode used in our calculation of the nonradiative recombination rates.\n",
    "\n",
    "The following code can be used to prepare the input files for the ab initio calculation of the configuration coordinate diagram (example for `VASP` is shown below)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "from pathlib import Path\n",
    "from shutil import copyfile\n",
    "from pymatgen.core import Structure\n",
    "from nonrad.ccd import get_cc_structures\n",
    "\n",
    "# equilibrium structures from your first-principles calculation\n",
    "ground_files = Path('/path/to/C0/relax/')\n",
    "ground_struct = Structure.from_file(str(ground_files / 'CONTCAR'))\n",
    "excited_files = Path('/path/to/C-/relax/')\n",
    "excited_struct = Structure.from_file(str(excited_files / 'CONTCAR'))\n",
    "\n",
    "# output directory that will contain the input files for the CC diagram\n",
    "cc_dir = Path('/path/to/cc_dir')\n",
    "os.mkdir(str(cc_dir))\n",
    "os.mkdir(str(cc_dir / 'ground'))\n",
    "os.mkdir(str(cc_dir / 'excited'))\n",
    "\n",
    "# displacements as a percentage, this will generate the displacements\n",
    "# -50%, -37.5%, -25%, -12.5%, 0%, 12.5%, 25%, 37.5%, 50%\n",
    "displacements = np.linspace(-0.5, 0.5, 9)\n",
    "\n",
    "# note: the returned structures won't include the 0% displacement, this is intended\n",
    "# it can be included by specifying remove_zero=False\n",
    "ground, excited = get_cc_structures(ground_struct, excited_struct, displacements)\n",
    "\n",
    "for i, struct in enumerate(ground):\n",
    "    working_dir = cc_dir / 'ground' / str(i)\n",
    "    os.mkdir(str(working_dir))\n",
    "    \n",
    "    # write structure and copy necessary input files\n",
    "    struct.to(filename=str(working_dir / 'POSCAR'), fmt='poscar')\n",
    "    for f in ['KPOINTS', 'POTCAR', 'INCAR', 'submit.job']:\n",
    "        copyfile(str(ground_files / f), str(working_dir / f))\n",
    "        \n",
    "for i, struct in enumerate(excited):\n",
    "    working_dir = cc_dir / 'excited' / str(i)\n",
    "    os.mkdir(str(working_dir))\n",
    "    \n",
    "    # write structure and copy necessary input files\n",
    "    struct.to(filename=str(working_dir / 'POSCAR'), fmt='poscar')\n",
    "    for f in ['KPOINTS', 'POTCAR', 'INCAR', 'submit.job']:\n",
    "        copyfile(str(excited_files / f), str(working_dir / f))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before submitting the calculations prepared above, the INCAR files should be modified to remove the `NSW` flag (no relaxation should be performed).\n",
    "\n",
    "One of the nice features provided by the NONRAD code is the `get_Q_from_struct` function, which can determine the Q value from the interpolated structure and the endpoints. Therefore, we don't need any fancy naming schemes or tricks to prepare our potential energy surfaces.\n",
    "\n",
    "#### Extracting the Potential Energy Surface and Relevant Parameters\n",
    "\n",
    "Once the calculations have completed, we can extract the potential energy surface using the functions provided by NONRAD. The below code extracts the potential energy surfaces and plots them. Furthermore, it will extract the dQ value and the phonon frequencies of the potential energy surfaces. These are 3 input parameters for the calculation of the nonradiative capture coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from glob import glob\n",
    "from nonrad.ccd import get_dQ, get_PES_from_vaspruns, get_omega_from_PES\n",
    "\n",
    "# calculate dQ\n",
    "dQ = get_dQ(ground_struct, excited_struct) # amu^{1/2} Angstrom\n",
    "\n",
    "# this prepares a list of all vasprun.xml's from the CCD calculations\n",
    "ground_vaspruns = glob(str(cc_dir / 'ground' / '*' / 'vasprun.xml'))\n",
    "excited_vaspruns = glob(str(cc_dir / 'excited' / '*' / 'vasprun.xml'))\n",
    "\n",
    "# remember that the 0% displacement was removed before? we need to add that back in here\n",
    "ground_vaspruns = ground_vaspruns + [str(ground_files / 'vasprun.xml')]\n",
    "excited_vaspruns = excited_vaspruns + [str(excited_files / 'vasprun.xml')]\n",
    "\n",
    "# extract the potential energy surface\n",
    "Q_ground, E_ground = get_PES_from_vaspruns(ground_struct, excited_struct, ground_vaspruns)\n",
    "Q_excited, E_excited = get_PES_from_vaspruns(ground_struct, excited_struct, excited_vaspruns)\n",
    "\n",
    "# the energy surfaces are referenced to the minimums, so we need to add dE (defined before) to E_excited\n",
    "E_excited = dE + E_excited\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.scatter(Q_ground, E_ground, s=10)\n",
    "ax.scatter(Q_excited, E_excited, s=10)\n",
    "\n",
    "# by passing in the axis object, it also plots the fitted curve\n",
    "q = np.linspace(-1.0, 3.5, 100)\n",
    "ground_omega = get_omega_from_PES(Q_ground, E_ground, ax=ax, q=q)\n",
    "excited_omega = get_omega_from_PES(Q_excited, E_excited, ax=ax, q=q)\n",
    "\n",
    "ax.set_xlabel('$Q$ [amu$^{1/2}$ $\\AA$]')\n",
    "ax.set_ylabel('$E$ [eV]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting input parameters that we have extracted for our calculation of the nonradiative recombination coefficient are below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dQ = 1.68588 amu^(1/2) Angstrom, ground_omega = 0.03358 eV, excited_omega = 0.03754 eV\n"
     ]
    }
   ],
   "source": [
    "print(f'dQ = {dQ:7.05f} amu^(1/2) Angstrom, ground_omega = {ground_omega:7.05f} eV, excited_omega = {excited_omega:7.05f} eV')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Calculate the Electron-Phonon Coupling Matrix Element\n",
    "\n",
    "Before computing the el-ph matrix elements, it is highly suggested that you re-read the [original methodology paper](https://doi.org/10.1103/PhysRevB.90.075202) and the [code implementation paper](https://doi.org/10.1016/j.cpc.2021.108056) to make sure you understand the details.\n",
    "\n",
    "The most important criteria for selecting the geometry in which the el-ph matrix elements are calculated is the presence of a Kohn-Sham level associated with the defect in the gap. For the C substitution we are considering, when the geometry of the defect ($\\{Q_0\\}$) corresponds to the neutral charge state, a well-defined Kohn-Sham state associated with the defect is clear and sits in the gap. Therefore, we compute the el-ph matrix elements by expanding around this configuration.\n",
    "\n",
    "To perform this calculation with `VASP`, access to version 5.4.4 or greater is necessary. The calculation amounts to calculating the overlap $\\langle \\psi_i (0) \\vert \\psi_f (Q) \\rangle$ (where $Q = 0$ corresponds to the geometry $\\{Q_0\\}$ described above) as a function of $Q$ and computing the slope with respect to $Q$. The el-ph matrix element is then $W_{if} = (\\epsilon_f - \\epsilon_i) \\langle \\psi_i (0) \\vert \\delta \\psi_f (Q) \\rangle$. For each $Q$, one sets up the calculation by copying the `INCAR`, `POSCAR`, `POTCAR`, `KPOINTS`, and `WAVECAR` from $Q = 0$ to a new directory and sets `LWSWQ = True` in the `INCAR` file. The `WAVECAR` from the $Q$ configuration is copied to `WAVECAR.qqq`. This calculation produces the file `WSWQ`, which includes the overlap information for all bands and kpoints. These files can then be parsed to obtain the matrix element using NONRAD as below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from nonrad.ccd import get_Q_from_struct\n",
    "from nonrad.elphon import get_Wif_from_WSWQ\n",
    "\n",
    "# this generates a list of tuples where the first value of the tuple is a Q value\n",
    "# and the second is the path to the WSWQ file that corresponds to that tuple\n",
    "WSWQs = []\n",
    "for d in glob(str(cc_dir / 'ground' / '*')):\n",
    "    pd = Path(d)\n",
    "    Q = get_Q_from_struct(ground_struct, excited_struct, str(pd / 'CONTCAR'))\n",
    "    path_wswq = str(pd / 'WSWQ')\n",
    "    WSWQs.append((Q, path_wswq))\n",
    "\n",
    "# by passing a figure object, we can inspect the resulting plots\n",
    "fig = plt.figure(figsize=(12, 5))\n",
    "Wifs = get_Wif_from_WSWQ(WSWQs, str(ground_files / 'vasprun.xml'), 192, [189, 190, 191], spin=1, fig=fig)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We pass as input, the indices of the 3 valence bands. What we find is that the valence band that is pushed down in energy has the greatest el-ph matrix element. This makes sense because it is pushed down by the interaction with the defect state.\n",
    "\n",
    "**NOTE**: We highly recommend passing a figure object to view the resulting plot. This ensures that the value obtained is reasonable.\n",
    "\n",
    "The resulting values of the matrix elements are shown below. They are in units of eV amu$^{-1/2}$ $\\unicode{xC5}^{-1}$. The VBM of wz-GaN has three (nearly degenerate) bands, so we must average over the matrix elements. The resulting value can then be directly input into the nonradiative capture calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(189, 0.08081487879834824), (190, 0.020450559002109615), (191, 0.0259145184003146)] 0.05040116487612406\n"
     ]
    }
   ],
   "source": [
    "Wif = np.sqrt(np.mean([x[1]**2 for x in Wifs]))\n",
    "print(Wifs, Wif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Alternative Method (Note: not publication quality)\n",
    "\n",
    "Another method for obtaining the Wif value would be to use the pseudo-wavefunctions from the `WAVECAR` files. This will neglect the core information. For some defect systems, this is not a bad approximation. The quality of the result can generally be judged by the overlap at $Q = 0$. If the overlap is almost zero (maybe < 0.05), then the result should be reasonably reliable. Please only use this to get a rough idea, the above method is preferred. This is facilitated by the `get_Wif_from_wavecars` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from nonrad.elphon import get_Wif_from_wavecars\n",
    "\n",
    "# this generates a list of tuples where the first value of the tuple is a Q value\n",
    "# and the second is the path to the WAVECAR file that corresponds to that tuple\n",
    "wavecars = []\n",
    "for d in glob(str(cc_dir / 'ground' / '*')):\n",
    "    pd = Path(d)\n",
    "    Q = get_Q_from_struct(ground_struct, excited_struct, str(pd / 'CONTCAR'))\n",
    "    path_wavecar = str(pd / 'WAVECAR')\n",
    "    wavecars.append((Q, path_wavecar))\n",
    "    \n",
    "# by passing a figure object, we can inspect the resulting plots\n",
    "fig = plt.figure(figsize=(12, 5))\n",
    "Wifs = get_Wif_from_wavecars(wavecars, str(ground_files / 'WAVECAR'), 192, [189, 190, 191], spin=1, fig=fig)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the results are reasonably close because the Q = 0 value is somewhat low."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(189, 0.08609599795923484), (190, 0.030574033957316595), (191, 0.019013362685731866)] 0.05387887767217285\n"
     ]
    }
   ],
   "source": [
    "print(Wifs, np.sqrt(np.mean([x[1]**2 for x in Wifs])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Compute Scaling Parameters\n",
    "\n",
    "When calculating the capture coefficient, we need to take into account two effects. First is the coulombic interaction between the carrier and defect. This occurs when the carrier is captured into a defect with a non-zero charge state. Second, there is the effect on the el-ph matrix element as a result of using a finite-size charged supercell. This leads to a suppression or enhancement of the charge density near the defect and would not occur in an infinitely large supercell.\n",
    "\n",
    "#### Sommerfeld Parameter\n",
    "\n",
    "The Sommerfeld parameter captures the long-range coulombic interaction that can affect the capture rates. The interaction can be attractive or repulsive and may enhance or suppress the resulting rate.\n",
    "\n",
    "For our system, we have the C substitution capturing a hole in the negative charge state, so there will be a long-range coulombic attraction that enhances the capture rates. One input parameter for the Sommerfeld parameter is the Z value. We define it as $Z = q_d / q_c$, where $q_d$ is the charge of the defect and $q_c$ is the charge of the carrier. For a negatively charge defect ($q_d = -1$) interacting with a hole ($q_c = +1$), we have $Z = -1$. $Z < 0$ is an attractive center, while $Z > 0$ is a repulsive center.\n",
    "\n",
    "Below, we calculate the scaling coefficient. Note, we use the hole effective mass (because we are capturing a hole) and the static dielectric constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sommerfeld Parameter @ 300K: 7.77969\n"
     ]
    }
   ],
   "source": [
    "from nonrad.scaling import sommerfeld_parameter\n",
    "\n",
    "Z = -1\n",
    "m_eff = 0.18 # hole effective mass of GaN\n",
    "eps_0 = 8.9  # static dielectric constant of GaN\n",
    "\n",
    "# We can compute the Sommerfeld parameter at a single temperature\n",
    "print(f'Sommerfeld Parameter @ 300K: {sommerfeld_parameter(300, Z, m_eff, eps_0):7.05f}')\n",
    "\n",
    "# or we can compute it at a range of temperatures\n",
    "T = np.linspace(25, 800, 1000)\n",
    "f = sommerfeld_parameter(T, Z, m_eff, eps_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Charged Supercell Effects\n",
    "\n",
    "Ideally, one could always calculate the el-ph matrix elements in the neutral charge state, and for many defects, this is possible. However, sometimes it is unavoidable to use a charged defect cell for computing the matrix elements. As a result of the charge on the supercell, an interaction between the defect and the delocalized band edges occurs. This leads to an enhancement or suppression of the charge density near the defect that would not exist in an infinite-size supercell, and therefore, a scaling of the el-ph matrix element.\n",
    "\n",
    "For the C substitution that we are considering, the el-ph matrix element is computed in the neutral charge state, so *no correction is necessary*. For illustration purposes, we shall examine how we would compute this scaling coefficient *if it were necessary* by studying the wavefunctions in the negative charge state. Here, we have a spurious interaction that suppresses or enhances the charge density of the bulk wavefunctions near the charged defect. The scaling coefficient is calculated by comparing the radial distribution of the charge density to a purely homogenous distribution. The function `charged_supercell_scaling` computes the scaling factor.\n",
    "\n",
    "Below is an example of the interaction with the valence band:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scaling = 0.9259259259259259\n"
     ]
    }
   ],
   "source": [
    "from nonrad.scaling import charged_supercell_scaling\n",
    "\n",
    "wavecar_path = str(excited_files / 'WAVECAR')\n",
    "\n",
    "fig = plt.figure(figsize=(12, 5))\n",
    "factor = charged_supercell_scaling(wavecar_path, 189, def_index=192, fig=fig)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print('scaling =', 1 / factor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The left-most plot is of the cumulative charge density (blue) against a homogenous distribution (red). The scaling parameter that brings the two into agreement is shown in the second plot. A plateau is found around ~2-3 $\\unicode{xC5}$. This is the value that we use for the scaling. If we had calculated the el-ph matrix elements in the negative charge state, we would scale the capture coefficient by 1 over this value squared (printed above). For completeness, the right-most plot is the derivative of the scaling coefficient, which provides an algorithmic way to find the plateau.\n",
    "\n",
    "Below we show the process for the interaction with the conduction band."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scaling = 1.4492753623188408\n"
     ]
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12, 5))\n",
    "factor = charged_supercell_scaling(wavecar_path, 193, def_index=192, fig=fig)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print('scaling =', 1 / factor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that the distribution is suppressed near the defect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Compute the Nonradiative Capture Coefficient\n",
    "\n",
    "We are now ready to compute the capture coefficient. The last input parameter we need to think about is the configurational degeneracy. For a C substitution, there are 4 identical defect configurations (one along each bond) that the hole can be captured into."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hi7/qSKQR5jAO9wiohSYeTpjLWWQiTdFsQTbV1dNElSm/SI8Jy8OwNzoVnw8JwpPtfVVHIg0xh3FYCIEXHq6PuLQcbDmdrDoOEVUSzRZkIq3LL9Lj2RXHsD8mDV8MaYYRrX1URyIySY8G1Ebj2tXwza5oziITaQQLMpEGFRTrMfmnY/j7fCo+H9wMw0K8VUciMlk6ncCLjzREbFoOfuO9yESawIJMpDEFxXpM+ek4dp9LxaeDgzC8Ncsx0b30DKyFpp5OmLPrPPdFJtIAFmQiDSksLsFzP5/ArrMp+OixphjVhrdVEJWHEAKv9GiEhPQ8/BrG0/WILB0LMpFGFOlLMPWX49gZdXO3ijHt6qqORGRWujVyRysfF3z7VzTyi/Sq4xCREbEgE2lAkb4Ez688gT8ir+L9/gHcrYJMgjls81aaEAKvPtoIyVn5WHnkkuo4RGREmi3I5jYwE92vkhKJ1349hd8jruCdfgF4qqOf6khEAMxjm7fbdahfA+39q2Pe7gvILSxWHYeIjESzBdkcB2aiipJS4p2NEfjt5GW81rMRxndiOSZ6UK882hBpNwqwPPSi6ihEZCSaLchElk5Kic9+P4ufD1/C5G718NxD9VVHIrIIIb5u6NbIHQv+voDs/CLVcYjICFiQiSzUvN0xWLg3Fk+0q4vXezZSHYfIorzSoxEyc4uwZH+86ihEZAQsyEQWaMn+OHz5x3kMbumJmQMCIYRQHYnIogR5OaNnYC38sC8WmbmFquMQkYGxIBNZmDVHE/DBlkj0DKyFL4Y2g07HckxkDC/1aIgbhcVYtDdWdRQiMjAWZCILsvV0MmasP43ODWrgm1EtYW3F/8SJjKVxbScMaF4HSw7EIeV6vuo4RGRA/OlJZCH2RafixdUn0MrHFQufCIadtZXqSER3ZQnbbb7coyGK9RJzdkWrjkJEBsSCTGQBTidmYtKKY6jnXhWLn2oNR1tr1ZGI7skSttusW70KHm/rg1VHExCbekN1HCIyEM0WZEuYuSACgLi0HIz78ShcHG2x7Ok2cHawUR2JSFOmdm8AO2sdvvrjvOooRGQgmi3IljBzQZSSnY8nlxyGBLBifBvUcrJXHYlIc9yr2WFCZ39sDU/GqYRM1XGIyAA0W5CJzN31/CKMXXIU124UYslTreHvXlV1JCLNmtDFH9Wr2OKz389CSqk6DhE9IBZkIjOUX6THxOVhiL6ajfljgtHC20V1JCJNq2pnjWnd6yM09hr2RqepjkNED4gFmcjM6EskXl5zEodi0/HlsObo2tBddSQiAjC6bV14uzng89/PoqSEs8hE5owFmciMSCkxc/MZbAu/grf7NsFjLT1VRyKiW2ytdXj10UaITL6Ozacvq45DRA+ABZnIjCzeH4floRcxobMfnunsrzoOEd2mf7M6CPBwwpd/nENhcYnqOER0n1iQiczE7+HJ+HhbFPoE1cYbvZuojkNEd6DTCUzv3RgJ6Xn4+fBF1XGI6D6xIBOZgeOXMvDi6pNo6e2C/wxvAZ1OqI5E9MAsdT/6Lg1qoEO96vhmVzSy8opUxyGi+8CCTGTiLl3LxYRlYajlZI/vnwyBvQ2PkCbLYKn70Qsh8GafJsjMK8J3u2NUxyGi+8CCTGTCMnML8dTSI9BLiaXjWqN6VTvVkYioHJp6OmNoKy/8eCAel67lqo5DRBWk2YJsqR/tkeUoKNZj4opjSEzPw6InQngQCJGZebVnI1jpBD7fflZ1FCKqIM0WZEv9aI8sg5QS09eexpG4dMwa1gxt/NxURyKiCqrlZI9nu948gvrYxXTVcYioAjRbkIlM2eyd0fjt5GW81rMRBrbgXsdE5mpiF3/UcrLDB1uieHgIkRlhQSYyMZtPXcacXdEYGuyFKd3qqY5DRA/A0dYarz7aCKcSMnl4CJEZYUEmMiGnEzPx6q+n0NrXFR8PagohuJ0bkbkb0soLgXWc8MX2c8gv0quOQ0TlwIJMZCKuXs/HhOVhqFHVDvPHBMPOmtu5EVkCnU7grb5NkJSZhyUH4lTHIaJyYEEmMgH5RXpMXB6G7Pxi/DA2BDW4nRuRRelQrwYeaVIL3+2+gLQbBarjENE9sCATKSalxGtrT+N0UhZmj2iBJh5OqiMRkRG80acx8ov0+OqPc6qjENE9sCATKTZvdww2n7q5Y8WjgbVVxyEiI6nnXhVPtvfFqqMJiEjiHvxEpowFmUih7RFX8OUf5zGopScmd+WOFUSW7sUeDVC9ii3e23QGUnLbNyJTxYJMpEjk5et4afVJtPB2waeDg7hjBWmOFk80dbK3wes9G+PYxQxsPMlt34hMFQsykQKZuYV49qcwODlYY9ETwbC34Y4VpD1aPdF0aLAXmnk545NtUbhRUKw6DhHdAQsyUSXTl0hMW3kCV7MKsGBMMGo62auORESVSKcTeH9AIFKyCzBvd4zqOER0ByzIRJXsqz/OYV90GmYODERLH1fVcYhIgVY+rhjSyguL98UhLi1HdRwiug0LMlEl+j08Gd/tuYBRbXwwqo2P6jhEpND0Xo1ga63DR1siVUchotuwIBNVkvNXs/HKr6fQ0scF7w8IUB2HiBSr6WSP5x+uj11nU7D7bIrqOERUCgsyUSXIyivCsyuOwdHWGvMf5zHSRHTTUx384F+jCj7YEomCYr3qOER0i2YLsha3FyI1SkokXl59EgnpuZg/phVqO3NRHhHdZGutw7v9AxCXloMf9sWpjkNEt2i2IGt1eyGqfN/8FY1dZ1PwTr8AtPZ1Ux2HiExMt0Y10TOwFr79KxoJ6bmq4xARNFyQiSrD7nMpmL0zGkNaeeHJ9nVVxyEiE/Ve/0DohMDMzWdURyEiANb3eoEQojxTXiVSykwD5CGyGEmZeXhp9Uk08XDCx4Oa8qQ8eiAciy1bHRcHvPhIA3yy7Sz+OHMFjwbWVh2JSNPuWZABXL71uNtPdysA3LOK6JbC4hI89/NxFOslvnu8FU/KI0PgWGzhxnX0w7pjSZi5ORKdGtSAo215fkQTkTGU5xaLKCmlv5TSr6wHgGvGDkpkTj7ZFoWTCZmYNbQZ/GpUUR2HLAPHYgtnY6XDR4OaIikzD3N2RauOQ6Rp5SnI7Q30GiJN2Ho6GUsPxmNcR1/0DvJQHYcsB8diDWjt64ZhwTdP2Dt3JVt1HCLNumdBllLmG+I1RFoQm3oD09edRksfF7zRu4nqOGRBOBZrxxt9mqCqvTXe+S0CUkrVcYg0qUK7WAghphsrCJG5yy/SY8rPx2FtJTB3dCvYWnOTGDIOjsWWza2KLWb0aowj8elYdzxJdRwiTbrrCgAhxJrSTwG0APC5URMRmal3N0bg7JVs/DiuNTxdHFTHIQvCsVh7hod4Y01YAj7ZFoWHG9eEaxVb1ZGINOVeU1zXpZTDbz2GAdhZGaGIzM2vYQlYE5aIad3r46FGNVXHIcvDsVhjdDqBTwYH4XpeET7aGqU6DpHm3Ksgf3zb87eMFYTIXEVfzcY7GyPQoV51vPhIQ9VxyDJxLNagxrWdMKlrPaw7noh90amq4xBpyl0LspQyDgCEEDVuPU+vjFBE5iK/SI+pv5xAFVtrzB7RAlY6HgZChmepY7EQor8QYlFWVpbqKCZravf68K9RBW9uCEduYbHqOESaUd5VREuMmoLITH20NRLnrmbjq+HNUdPJXnUcsnwWNRZLKTdLKSc6OzurjmKy7G2s8OngICSk5+HrP8+rjkOkGeUtyJwWI7rN9ohk/HToEiZ28Uc33ndMlYNjsQa19a+O0W19sHh/HE4n8iRxospQ3oLMjRiJSknKzMPra0+juZczXn20keo4pB0cizVqRu/GqFHVDtPXhaNIX6I6DpHF4wwyUQUV60vwwsoTKJHAN6Nacr9jqkwcizXKyd4GHz7WFFHJ1/H9vljVcYgsXnl/sr9h1BREZmTOrmiEXczAx4Oaom71KqrjkLZwLNawnoG10btpbczeGY24tBzVcYgsWrkKspQyQggxTAhRDQCEEG8LIdYLIVoZNx6RaTl4IQ1zd8dgaLAXBrbwVB2HNIZjMc0cEAg7ax2mrzuNkhLecUNkLBX5bPgdKWW2EKITgEcALAYw3zixiExPek4hXlp9En41qmDmgEDVcUi7OBZrWE0ne7zTNwBH4tKxPDRedRwii1WRgqy/9b99ASySUm4FwLMvSROklHh97Slk5BTh21EtUcXurqe0ExkTx2KNGxbihW6N3PH59nOI560WREZRkYKcJIRYCGAEgG1CCLsKfj2R2frlyCXsjErB9N6NEViHe7aSUhyLNU4IgU8HB8HaSuC1tad4qwWREVRkUB0OYAeAnlLKTABuAF4zSioiExKbegMfbYlC5wY1MK6Dr+o4RByLCR7ODnivfyCOxmfgx4PxquMQWZxyf04spcwFsL7U82QAycYIRWQqivQleGn1SdjZ6PDlsObQ8ShpUoxjMf1jSCtPbAtPxqwdZ/FQI3f4u1dVHYnIYvBjOaK7+HZXNE4lZuGTQUGoxaOkiciE/HOrha2VDq+tPQ09b7UgMhiLKshCiAAhxBohxHwhxFDVeci8HbuY/v9buvUJ8lAdh4jof9Ryssf7AwJx7GIGluyPUx2HyGKYTEEWQiwRQqQIISJuu95LCHFOCBEjhJhxj7fpDeBbKeVkAE8aLSxZvBsFxXhx9UnUcXHAe/0DVMchIirToJaeeKRJLXz5xznEpNxQHYfIIty1IAshJgkhlgshRgohtgghJhsxy1IAvW77/lYA5uFm8Q0AMOrWLHHQrTylHzUBrAAwUggxC0B1I2YlCzdz0xkkZeTh6xEtUM3eRnUc0rhKHovJzAgh8MngpnCwtcLLa06iSF+iOhKR2bvXDHJ3AGMBPCGl7AegubGCSCn3Aki/7XIbADFSylgpZSGAVQAGSinDpZT9bnuk3Ho8B2AGgLSyvpcQYqIQIkwIEZaammqsPxKZqe0Ryfj1WCKmdKuP1r5uquMQAZU4FpN5qlnNHp8MCsLpxCx8uytadRwis3evgnxNSikBLLj1vMDIeW7nCSCh1PPEW9fuSAjhK4RYBGA5gFllvU5KuUhKGSKlDHF3dzdYWDJ/V6/nY8b6cDTzcsYLjzRQHYfoH6rHYjIDfYI8MKSVF+bujsGxi7fPNxFRRdyrIM8BACnl5lvP19/ltcpJKeOllBOllI9LKferzkPmRUqJ6etOI79Ij69HtICNlcncok9kVmMxqfP+gADUcXHAS6tP4UZBseo4RGbrrg1ASnn2tud/GzfO/0gC4F3qudeta0QGt/poAvacS8WMXo1Rj/uJkgkxgbGYzEQ1exv8Z3gLJGbk4oPNZ1THITJb5Z4iE0KECCE2CCGOCyFOCyHChRCnjRkOwFEADYQQfkIIWwAjAWwy8vckDUrMyMVHW6PQ3r86nmzvqzoOUZkUjcVkRtr4uWFyt3pYE5aI7RE8Q4bofpT7JD0AP+PmcabhAAy+RFYIsRJANwA1hBCJAN6TUi4WQkzFzWNVrQAskVIa5FdiIUR/AP3r169viLcjM1ZSIvH62tOQUuKLoc14Wh6ZOqOOxWQZXni4IfaeT8Mb68PRyscVNXnQEVGFVOQmy1Qp5SYpZZyU8uI/D0MFkVKOklJ6SCltpJReUsrFt65vk1I2lFLWk1J+bMDvt1lKOdHZ2dlQb0lm6ufDF3HwwjW81TcA3m6OquMQ3YtRx2KyDLbWOnw9ogXyivR49dYEABGVX0VmkN8TQvwAYBdKraCWUnKxCJmti9dy8Mm2s+jS0B2j2njf+wuI1ONYTOVSv2ZVvNWnCd7ZeAZLD8ZjXEc/1ZGIzEZFCvI4AI0B2ODfj/UkuJqazFRJicRrv56GtZXA50OCIARvrSCzwLGYym1Mu7rYcy4Vn247i9a+bmjqyU9NicqjIgW5tZSykdGSEFWyJQficCQ+HV8Oaw4PZwfVcYjKi2MxlZsQArOGNUefOfswbeUJbJ7WCVXtKvKjn0ibKnIP8kEhRIDRklQyIUR/IcSirKws1VFIgQupNzBrxzk80qQmhrQq8+wZIlNkUWMxGZ9bFVvMHtkCF6/l4N3fIlTHITILFSnI7QCcFEKcs4SthbhIT7uK9SV4Zc0pONha4ZPBvLWCzI5FjRNN42oAACAASURBVMVUOdr5V8fzDzfA+hNJWHcsUXUcIpNXkc9ZehktBVEl+n5fHE4mZOKbUS1Rsxq3PiKzY9Jj8a3Z7fcBXAOwS0q5Vm0i+se07g0QeuEa3tkYgRY+LjwQieguyj2DXHo7IW4tRObqQuoNfL3zPHo3rY3+zTxUxyGqMGOOxUKIJUKIFCFExG3Xe92asY4RQsy4x9v0BvCtlHIygCcNkYsMw0onMGdkS9hZ6zD1lxPIL9KrjkRksipykt4yIYRLqeeuQoglxolFZHglJRLT156Gg40VZg4M5K0VZJaMPBYvxW0z1EIIKwDzcLP4BgAYJYQIEEIECSG23PaoCWAFgJFCiFkAqhsoFxlIbWd7fDW8OaKSr+PTbVGq4xCZrIrcYtFMSpn5zxMpZYYQoqURMlUKnqSnPSsOXUTYxQx8Oaw5b60gc2a0sVhKuVcI4Xvb5TYAYqSUsQAghFgFYKCU8lMA/cp4q+duFesyt54TQkwEMBEAfHx8HjA5VUT3xrUwvpMfFu+PQ1v/6ugTxE/TiG5XkUV6OiGE6z9PhBBuqFjBNilcpKctiRm5+Hz7zQNBuGsFmbnKHos9ASSUep5469odCSF8hRCLACwHMKus10kpF0kpQ6SUIe7u7gYLS+UzvVdjtPB2wetrTyM29YbqOEQmpyIF+SsAoUKID4UQHwI4COAL48QiMhwpJd5YHw4B4JNBTXlrBZk7kx6LpZTxUsqJUsrHpZT7VeehO7O11mHe461gYyUw+afjyC0sVh2JyKRUZJHecgCDAVy99RgspVxhrGBEhrL2WCL2Radheu/G8HJ1VB2H6IEoGIuTAJQ+h93r1jUyc54uDpgzsiXOp2TjrQ0RkFKqjkRkMir0sZyUMhJApJGyEBlcSnY+PtwSida+rhjTtq7qOEQGUclj8VEADYQQfrhZjEcCGF1J35uMrEtDd7z4cEN8vfM8guu6Ykw7jpNEQDlmkIUQxw3xGiIV3v3tDPKLS/DZkGbQ6XhrBZmvyhiLhRArAYQCaCSESBRCjJdSFgOYCmAHgCgAa6SUZx7k+5T6fjzR1ARM614fXRu644PNkTidmHnvLyDSAHGvj1SEEHkAou/2EgDOUkqzWoZcaheLCdHRd/vjkbn6PTwZk38+jum9GmNyt3qq4xD9FyHEMSllSAVeb5FjMQCEhITIsLAw1TE0LSOnEP2+vXnL+JZpneBaxVZxIqLKUdZYXJ5bLBqX4zVmt9u4lHIzgM0hISETVGchw8vMLcQ7G8+gqacTJnT2Ux2HyBAsciwm0+BaxRbzHm+FYQsO4qU1J7FkbGt+6kaads+CzNPyyBx9uCUKmbmFWP50G1hbVWSzFiLTxLGYjK2Ftwve7R+Id36LwH/+PI9XezZSHYlIGTYHsjj7o9Ow7nginu3qj4A6TqrjEBGZjTFtfTA8xAtzd8dgW3iy6jhEyrAgk0XJL9Lj7d/C4VvdEdO6N1Adh4jIrAgh8OFjTdHSxwWv/noKZ69cVx2JSIkHKshCiOqGCkJkCHP/ikH8tVx8PCgI9jZWquMQVQpzHYu5i4VpsrO2woIxwahqZ40Jy8OQkVOoOhJRpbvvgiyEWAfgIyHEz0KIhwyYiei+nL+ajQV/X8DgVp7oWL+G6jhElcKcx2Ip5WYp5URnZ2fVUeg2tZzssfCJYFzNKsDUlcdRrC9RHYmoUj3IDPJZKeVkKeXjAIYaKhDR/SgpkXhzfTiq2VvjrT5NVMchqkwci8koWvq44qNBTXEg5ho+/f2s6jhElapCJ+ndppcQIh3AKQC5BspTaUrtg6w6ChnAqqMJCLuYgVlDm6F6VTvVcYgqk1mPxWTahod4I/LydSzeH4cADycMCfZSHYmoUpTnJL13hBDP3eH/6oWbpyp1BOAphFhm6HDGxI/2LEdKdj4++z0K7fzdMJSDN1koSx2LyfS91bcJ2vtXxxsbwnH8UobqOESVojwzyMMBtL7D9YEA3KWUMw0biahiPtwShfyiEnw8KAhCcGN7slgci0kJGysd5j3eCoO+O4CJy8OwYUpHeLs5qo5FZFTluQe5SEqZf4frKwCMMXAeogrZcy4Fm09dxnMP1Uc996qq4xAZk8WNxdzFwny4VbHF4rGtUVhcgvHLjuJ6fpHqSERGVZ6CXCiE8Lj9opSyAAD/CyFl8gr1ePu3CNRzr4JJ3fxVxyEyNosbi3mrm3mpX7Mq5o8JRmxqDqb+coI7W5BFK09B/grARiFE3dIXhRA1AUijpCIqh9m7ziMxIw+fDAqCnTX3PCaLx7GYlOtYvwY+fKwp9p5PxczNkZCSf/XIMt3zHmQp5a9CCEcAx4QQhwCcxM1iPQzA+8aNR3RnUcnX8cO+OIwI8UZbf7M8I4GoQjgWk6kY1cYHcWk5WLQ3Fv7uVTCuo5/qSEQGV659kKWUywD4AVgNwAZAPoDRUsqfjZiN6I5KSiTe2hAOFwcbvNGnseo4RJWGYzGZium9GqNHQC18uCUSf529qjoOkcGVex9kKWU2bi4GIVJq7bFEHL+UiS+HNYeLo63qOESVimMxmQIrncCckS0wbEEopv1yAqufbY+mnryXnCzHg5ykZ9a4eto8ZeQU4tPfo9Da1xVDWnmqjkNEpFmOttZYPLY1nB1sMG7pUSSk85washyaLchcPW2evthxDtfzi/HhY0255zGRmeNEhfmr7WyPZU+3QUGRHmN/PIKMnELVkYgMQrMFmczPiUsZWHX0EsZ18EXj2k6q4xDRA+JEhWVoUKsafhjbGokZeRi/7Cjyi/SqIxE9MBZkMgv6Eol3NkagZjU7vNijoeo4RERUShs/N8wZ0QInEjIxbeUJ6Eu4/RuZNxZkMgs/H76IiKTreLtvAKralXttKRERVZLeQR54v38g/oy8inc3RnCPZDJrbBpk8lKzCzBrxzl0ql8D/Zr9z0FiRERkIsZ28EVyVj4W/H0BHs72mNq9gepIRPeFBZlM3qfbopBfpMfMgYFcmEdEZOJe79kIV6/n48s/zqN6VTuMauOjOhJRhbEgk0k7HHsN608k4bmH6qGee1XVcYiI6B50OoHPhzRDRm4h3twQjmr21ujXrI7qWEQVwnuQyWQV6UvwzsYIeLo4YOpD/JiOiMhc2FrrMP/xYITUdcVLq09i97kU1ZGIKoQFmUzWjwficP7qDbw/IBAOtlaq4xCRgXEfZMvmYGuFxU+1RsNa1TD5p2M4EpeuOhJRubEgk0lKzsrD7J3ReLhxTfQIqKU6DhEZAfdBtnxO9jZY9nQb1HFxwPilRxGRxF+GyDywIJNJ+nBLJPQlEu8PCFQdhYiIHkCNqnb4aXxbODnYYOySI7iQekN1JKJ70mxB5kd7pmt/dBq2hV/Bcw/Vh7ebo+o4RET0gOq4OGDF+DYQAhjzw2EkpOeqjkR0V5otyPxozzQV6Uvw/uYz8HFzxMQu/qrjEBGRgfi7V8Xyp9sip6AYo384hMuZeaojEZVJswWZTNPy0IuISbmBd/oFwN6GC/OIiCxJQB0nrBjfFpk5RRj1/SFcycpXHYnojliQyWSk3SjA7D/Po0tDdzzSpKbqOEREZATNvV2wbHwbXLtRiFHfH0LKdZZkMj0syGQyZm0/h7wiPd7tF8AT84iILFgrH1csHdcaV6/nY9T3h5CaXaA6EtF/YUEmk3AqIRNrjiXg6U5+qF+TJ+YREVm6EF83/PhUa1zOzMfo7w8h7QZLMpkOFmRSrqRE4v3NZ1C9ih2mda+vOg4REVWStv7VsfipECRk5GLMD4eRnlOoOhIRABZkMgEbTiThxKVMzOjdGNXsbVTHIaJKwu02CQA61KuBH55sjbi0HIxcFIqUbN6TTOqxIJNS2flF+Gz7WbTwdsHglp6q4xBRJeJ2m/SPTg1q4MenWiMhPQ8jF3J3C1KPBZmUmvtXDFKzCzBzQCB0Oi7MIyLSqg71a2D5+DZIyS7A8IWhSMzgYSKkDgsyKXMh9QaWHIjD8BAvNPd2UR2HiIgUa+3rhp+eaYvM3EKMWHgI8Wk5qiORRrEgkxJSSnywORL21lZ4rWdj1XGIiMhEtPB2wS8T2iG3sBgjFoUiJuWG6kikQSzIpMSuqBT8fT4VLzzSAO7V7FTHISIiE9LU0xmrJraHvgQYuSgUZ69cVx2JNIYFmSpdfpEeH2yJRP2aVTG2g6/qOEREZIIa1a6G1c+2g7VOhxELD+HYxQzVkUhDWJCp0i3eH4dL6bl4r38AbKz4V5CIiO6snntV/DqpPVwdbTDmh8PYcy5FdSTSCLYTqlTJWXmY+1cMHg2ohc4N3FXHISIiE+ft5ohfJ3WAv3sVPLMsDBtPJqmORBqg2YLMDerV+Oz3s9BLibf7BqiOQkREZsK9mh1WTmyH4LqueHH1SSw7GK86Elk4zRZkblBf+Y7Gp2PjycuY1MUfPtUdVcchIiIz4mRvg2VPt0GPJrXw3qYz+PrP85BSqo5FFkqzBZkql75E4r2NZ1DH2R6Tu9VXHYeIiMyQvY0Vvnu8FYYFe2HOrmi8u/EM9CUsyWR41qoDkDasOnoJkcnXMXd0SzjYWqmOQ0REZsraSocvhjaDWxVbLNwbiyvX8/HNSP5sIcPiDDIZXWZuIb7ccQ5t/dzQN8hDdRwiMhFcC0L3SwiBN/o0wcwBgdgVdRUjF4UiNbtAdSyyICzIZHRf/3keWXlFeH9AIIQQquMQkYngWhB6UGM7+GLhEyE4dzUbg+cf4Kl7ZDAsyGRUZ69cx4pDFzGmXV008XBSHYeIiCxMj4BaWDWxPfIK9Rgy/yAOx15THYksAAsyGY2UEu9vOgMnBxu83KOh6jhERGShWni7YMOUjqhe1RZPLD6CTacuq45EZo4FmYxma3gyDsWm49VHG8HF0VZ1HCIismDebo5YP7kDWvi44PmVJzBvdwy3gaP7xoJMRpFbWIxPtkahiYcTRrXxUR2HiIg0wMXRFivGt8GA5nUwa8c5vLT6JPKL9KpjkRniNm9kFAv2XMDlrHzMHtkSVjouzCMiosphZ22FOSNboGGtqvjyj/OIu5aL758IRk0ne9XRyIxwBpkMLiE9Fwv2xmJA8zpo4+emOg4REWmMEAJTuzfAgjHBiL6ajQFzD+B0YqbqWGRGWJDJ4D7aGgkrIfBGn8aqoxARkYb1alob6yZ3gJVOYNiCUGzm4j0qJxZkMqh90anYceYqpnavDw9nB9VxiIhI45p4OGHj1I5o5uWMaStP4Ks/zqGEx1PTPbAgk8EU6Uswc3Mk6lZ3xPhOfqrjEBERAQBqVLXDT8+0xfAQL3z7VwwmLA9DVl6R6lhkwliQyWCWHYxHTMoNvN03APY2VqrjEBER/T87ayt8PqQZPhgYiL/Pp2LA3P2ISr6uOhaZKBZkMojU7ALM2RmNrg3d8UiTmqrjEBER/Q8hBJ5s74vVz7ZDfpEeg747gA0nElXHIhPEgkwGMWvHWeQX6/Fu/wAIwW3diIjIdAXXdcOWaZ3R3MsFL60+hXc3RqCwuER1LDIhLMj0wE4mZGJNWCKe7uiHeu5VVcchIiK6J/dqdvj5mbaY0NkPy0MvYuSiUFzJylcdi0wECzI9kJISifc2nYF7NTtM7V5fdRwiIqJys7bS4a2+AZg3uhXOXslGv2/34UBMmupYZAJYkOmBrDueiFMJmZjRqzGq2duojkNERFRhfZt5YONzHeHiaIsxiw/jqz/OoVjPWy60jAWZ7tv1/CJ8vv0sWvm4YFBLT9VxiIiI7luDWtWwaWpHDAu+uRXc6O8PIzkrT3UsUoQFme7bNzujcS2nEO8PCIROx4V5RERk3hxtrfHF0OaYPaIFzlzOQp85+7Ar6qrqWKQACzLdl5iUbCw9GI8RId5o5uWiOg4RmSEhRH8hxKKsrCzVUYj+y2MtPbF5Wid4ODtg/LIwfLQlkrtcaAwLMlWYlBIzN0fCwdYKr/VspDoOEZkpKeVmKeVEZ2dn1VGI/oe/e1Wsn9IBY9vXxQ/74zB0wUHEpt5QHYsqidkWZCGEvxBisRBibalrVYQQy4QQ3wshHleZz5L9EXkV+6LT8HKPhqhe1U51HCIiIqOwt7HCzIFNsWBMMC6l56LvN/vx06GLkFKqjkZGpqQgCyGWCCFShBARt13vJYQ4J4SIEULMuNt7SCljpZTjb7s8GMBaKeUEAAMMHJsA5Bfp8eGWSDSsVRVPtKurOg4REZHR9WpaGzte7ILWfm54+7cIjF8WhtTsAtWxyIhUzSAvBdCr9AUhhBWAeQB6AwgAMEoIESCECBJCbLntUdZZxl4AEm79s95I2TVt0d5YJGbk4f3+gbC2MtsPIIiIiCqklpM9lo1rjZkDAnEgJg09Z+/FH2euqI5FRqKk4Ugp9wJIv+1yGwAxt2aGCwGsAjBQShkupex32yOljLdOxM2SDJjx7SOmKikzD9/tiUGfoNroUL+G6jhERESVSgiBsR18sWVaJ3g422PiimOYvvY0cgqKVUcjAzOlEumJf2d/gZtlt8zNdYUQ1YUQCwC0FEK8cevyegBDhBDzAWy+y9dOFEKECSHCUlNTDRBdGz7ZGgUAeLNPE8VJiIiI1GlQqxo2TOmIKd3qYc2xBPSesw+HY6+pjkUGZEoFuUKklNeklJOklPWklJ/eupYjpRwnpZwspfz5Ll+7SEoZIqUMcXd3r7zQZmzv+VRsDU/G5K714eXqqDoOERGRUrbWOrzeqzFWT2wPABix6BDe2xjB2WQLYUoFOQmAd6nnXreukWIFxXq8t+kMfKs74tmu/qrjEBERmYw2fm7Y/mJnjOvoi+WHLqLn7L04GJOmOhY9IFMqyEcBNBBC+AkhbAGMBLBJcSYC8P3eWMSl5WDmwKawt7FSHYeIiMikONpa473+gVjzbHvYWOkw+ofDeHNDOLLzi1RHo/ukapu3lQBCATQSQiQKIcZLKYsBTAWwA0AUgDVSyjNGzMATnMohIT0X3/4Vg95Na6NrQ96OQkREVJbWvm7Y9nxnTOjsh5VHLqHX7H34+zzXOpkjVbtYjJJSekgpbaSUXlLKxbeub5NSNrx1X/HHRs7AE5zKYebmM7DSCbzTL0B1FCIiIpPnYGuFt/oGYO2kDrC30WHskiN4YdUJ7ptsZkzpFgsyMX9GXsXOqBS88HAD1HFxUB2HiIjIbATXdcXW5zvjhYcb4PfwK3j4qz1YeeQSSkp4Cp85YEGmO8or1OP9TWfQoGZVPN3JT3UcIiIis2NvY4WXejTEthc6o4mHE95YH47hC0Nx/mq26mh0DyzIdEdzd0cjKTMPHz7WFDY8MY+IiOi+1a9ZFasmtsOsoc1wIfUG+szZh1k7ziK/iIf+mirNNh8u0ivbhdQbWLQ3FoNaeqKdf3XVcYiIiMyeEALDQryx65VueKylJ+btvoBHv96LnZFXISVvuzA1mi3IXKR3Z1JKvLsxAvY2VnijT2PVcYiIiCyKWxVbfDmsOX6Z0Ba21jo8szwM45YeRWzqDdXRqBTNFmS6s/XHk3Ag5hpe69kINavZq45DRERkkTrUq4HfX+iMt/s2wbH4DPScvRef/h6FGzyJzySwINP/u3ajAB9tjUQrHxeMaVtXdRwiIiKLZmOlwzOd/bHr1a54rIUnFv4di+5f7sGGE4m87UIxFmT6fx9tvfmb62dDmkGnE6rjEBERaULNavaYNaw5NkzpAA9ne7y0+hSGLghFeCLXSami2YLMRXr/be/5VGw4kYTJXeuhYa1qquMQERFpTksfV2yY0hFfDGmG+LQc9J+7Hy+tPomkzDzV0TRHswWZi/T+lVtYjLd+C4e/exVMeai+6jhERESapdMJDG/tjd2vdcPkbvWwNTwZD325B59vP4vr+UWq42mGZgsy/Wv2zmgkpOfh00FBsLexUh2HiIhI85zsbTC9V2PsfrUb+gV5YP6eC+g2aw+WHYxHkb5EdTyLx4KscRFJWVi8Pw6j2nijLfc8JiIiMimeLg74z4gW2Dy1ExrVqob3Np3Bo1/vxfaIZC7kMyIWZA0rLC7Ba2tPw62KLWb0aqI6DhEREZUhyMsZv0xoiyVPhcBKJzDpp+N4bN4B7D2fyqJsBCzIGjb3r2hEJV/HJ4OC4OxoozoOERER3YUQAt0b18L2Fzrji6HNkHajEE8uOYKRiw4hLD5ddTyLotmCrPVdLMITszBvzwUMbuWJHgG1VMchIiKicrK20mF4iDf+erUrZg4IxIXUHAxdEIqnfjyCiCRt9hpD02xB1vIuFgXFerzy60nUqGqL9/oHqo5DRERE98HO2gpjO/hi7+vdML1XY5y4lIl+3+7HlJ+P4fzVbNXxzJq16gBU+WbvjMb5qzfw47jWcHbgrRVEdP+EEP4A3gLgLKUceutaFQDfASgEsEdK+bPCiEQWz9HWGpO71cPj7Xzww744LN4Xi98jrqB309qY+lADBNRxUh3R7Gh2Bvl+ZOYWYs7OaCRnme+G3ccvZWDh3xcwIsQbDzWqqToOESkkhFgihEgRQkTcdr2XEOKcECJGCDHjbu8hpYyVUo6/7fJgAGullBMADDBwbCIqg5O9DV7u0RD7pnfHc93qY9/5NPT5Zh+eWRaG04mZquOZFRbkCsjOL8acXeex9GC86ij35UZBMV5cdRIezg54ux93rSAiLAXQq/QFIYQVgHkAegMIADBKCBEghAgSQmy57VHWb9leABJu/bPeSNmJqAxuVWzxas9G2D+jO156pCGOxqdjwNwDGLvkCI5d5GK+8mBBrgBvN0f0buqBXw5fwo2CYtVxKuzdjRFIzMjF7JEtUM2et1YQaZ2Uci+A239atgEQc2tmuBDAKgADpZThUsp+tz1SynjrRNwsyUAZP2eEEBOFEGFCiLDU1FRD/HGI6DbODjZ44ZEG2D/9IbzeqxHCk7IwZH4oRn9/CAdj0rg93F2wIFfQM539kJ1fjNVHE+79YhOy8WQS1h9PwrTuDdDa1011HCIyXZ74d/YXuFl2Pct6sRCiuhBiAYCWQog3bl1eD2CIEGI+gM13+jop5SIpZYiUMsTd3d1A0YnoTqrZ22BKt/rYP/0hvNWnCc5fvYHRPxxG/7n7senUZRTzZL7/wUV6FdTSxxUhdV2xZH8cnmhXF7bWpv87RkJ6Lt7eEIGQuq6Y1r2+6jhEZEGklNcATLrtWg6AcWoSEVFZHG2tMaGLP55oXxcbTiTh+32xeH7lCXzh6oDxnfwwPMQbVexYDQENzyA/yD7Iz3Wvj6TMPKw+eskIyQyrsLgEz686AQhg9sgWsLbS7L9yIiqfJADepZ573bpGRBbC3sYKo9r4YOdLXfH9kyHwcLbHzM2R6PDZX5i14yxSsvNVR1ROs23pQfZB7tbQHW183fDNXzHILTTte5E/3hqJE5cy8dngZvBydVQdh4hM31EADYQQfkIIWwAjAWxSnImIjECnE+gRUAu/TuqA9VM6oL1/dXy35wI6fb4bM9adxtkr11VHVEazBflBCCHweq9GSM0uwOJ9carjlOm3E0lYFnoREzr7oW8zD9VxiMjECCFWAggF0EgIkSiEGC+lLAYwFcAOAFEA1kgpzxjp+2v6RFMiU9LKxxULngjGX690w7BgL2w4kYRes/dh5KJQbI9I1tx9ykLrKxhDQkJkWFjYfX3tlJ+PYVdUCna+3BXebqY1OxuVfB2DvjuAZl4u+OWZtry1gsjECCGOSSlDVOcwBQ8yDhORcWTkFGJ1WAJWhF5EUmYePF0cMKZdXYxs7Q3XKraq4xlMWWMxW9MDeKdfAKx0Au9tOmNSW6Vk5BRi0k/H4GRvg7mjW7IcExERUYW4VrHFpK71sPf1h7DwiWDUre6Iz7efRbtPd+H1tacQkWTZn/xwqeID8HB2wEuPNMTH26KwLfyKSdzGUFCsx7MrjiE5Kx8rJ7RFzWr2qiMRERGRmbLSCfQMrI2egbVx7ko2loXGY8PxJKwJS0RzL2eMbuuDfs3qWNzuF5xafEBPdfRFcy9nvLkhHFey1K76lFJixrpwHIlPx5fDmiO4Lvc7JiIiIsNoVLsaPhkUhENvPIz3+gcgt1CP6evC0faTXXhrQ7hFzSqzID8gGysdvh7RAoXFJXjl15MoKVF3q8XsndHYcCIJr/VshAHN6yjLQURUHlykR2SenB1tMK6jH/54qQvWTmqPRwNrYe2xRPT7dj8Gzt2PVUcuIccMTxwujQXZAPzdq+Ld/gE4EHMNs3eeV5Jh8f44zNkVjWHBXpjSrZ6SDEREFfEg220SkXpCCIT4uuE/w1vgyJuP4P3+Acgr0mPG+puzyq+vPYUjcekmtU6rvCzrhpEKEEL0B9C/fn3DnCw3srU3TlzKwDd/xaBRbadKvR/5p0MX8eGWSPRuWhufDg6CEKLSvjcRERGRs6MNnuroh7EdfHH8UgZWHknAltPJWBOWCB83Rwxu5YkhrbxMbtevsnCbNwNuL1RQrMfo7w/jzOUsrJzQDi19XA3yvnez6sglzFgfju6Na2LBmGCzOPqaiLjNW2nc5o3IMuUWFmN7xBWsPZaI0NhrkBJo6+eGIcFe6BPkgaomsLCvrLGYBdnAA3NKdj6GLQhFRk4hfpnQDk09jfPRoZQS8/++gC+2n0PXhu5Y+EQw7G2sjPK9iMjwWJD/xYJMZPmSMvOw4Xgi1h1PQlxaDhxsrNCraW0MaFEHnerXgI2iLWlZkMtgjIE5MSMXwxeEIq9Ij5+eaYvAOoYtycX6Eny0NQpLD8ZjYIs6mDW0OWeOicwMC/K/WJCJtENKieOXMrHueCK2nLqM6/nFcHW0Qe8gD/RvVgdt/Nxgpau8W0VZkMtgrIE5Pi0Ho74/hOt5RfhuTDC6NnQ3yPum3SjA1F+O41BsOsZ38sNbfZpAV4l/kYjIMFiQ/2styITo6GjVcYiokhUU67HvfBo2nbqMPyOvIq9Ij5rV7NC3mQcGNK+DFt4uRl9XxYJcBmPOXCRn5WHcj0cRnXIDL/do6bUCAAAADFhJREFUiEld6z3Qb0V/Rl7FWxvCkZVXhE8HB2FwKy8DpiWiysSC/C/OIBNRbmEx/jqbgk0nL2PPuVQU6kvg5eqA/s3roE9TDzT1dDJKWWZBLoOxB+bs/CK8sT4cW04no62fGz4Y2BSNaler0HskpOfiix3nsPnUZTSuXQ3/Gd4CAXWcjJSYiCoDC/K/WJCJqLTr+UX448xVbDp1GQdi0qAvkfB0ccCj/9fevcfYUZZxHP/+6NKFXmyhlILdxi20UkuVchGLGC1VoKCCicZAvFtDNHiNiQE1Ev4gxsSIGI2KgsRLwIiotSZUrBiNECiFqku3hRYLXYRuS6FIuXTbPv4x77LD6Tm73XXPzLn8PsmkM++ZyzNnpu88+847c06exfKTj+OM7vHrhuEEuYYiKuaI4Ffr+rjmD73898UB3ntaFx89u3vEvsk9j+/mF/c8yq3r+pDE5Uvn8amlJ7q/sVkLcII8xAmymdWya89e/tS7ndU9T/K3zTvZu+8AMyZP5NyFszh/0XG8+cQZdHaM/SUFTpBrKLJifnrPXq5b8zC3rH2MFwcOcNKsqbx53gzmHzuVGVMmEgE7nnuJjU88y91bnuKRnXvo7DiM957exWeWzeP4aUcWEqeZ1Z8T5CFOkM3sUDz30j7+sqmf23ue5M6N/ezZu5+pnR2cs+BYli86jre9diaTR/nqOCfINZRRMe9+foDbHuhjTW8/a7fu4qV9B17x+ZTODt7YfRTnLDiWi0+ZzbRJhxcan5nVnxPkIU6QzWy0XhzYz11bdrK6Zzt39G5n1569XP+h0znv5ONGtZ5adXH5b2huQ4O/Yf6xs+ey/0DwxO4XeOb5AQBmTu1k5pROv5nCzMzMrIYjDp/AsgWzWLZgFtfsP8B9jz7N4jnTx239TpBLNuEw0XXUJLrq/6N7ZmYNJfeat7JDMbMm1jHhMJacMGNc19m2T3tJerek63fv3l12KGZmbSkifh8Rl02bVp9fHDUzG6u2TZBdMZuZmZlZNW2bIJuZmZmZVeME2czMzMwsxwmymZmZmVmOE2QzMzMzsxwnyGZmZmZmOU6QzczMzMxynCCbmVkp/D56M2tUTpDNzKwUfh+9mTUqJ8hmZmZmZjmKiLJjKJWkHcCjuaJjgJ0lhZPnOBorBnAcjRYDNHccr4mImfUIptlUqYdbWaOcs0Vqt31ut/2F5t7nqnVx2yfIlSTdFxFnOI7GiaMRYnAcjReD47Bm1I7nSrvtc7vtL7TmPruLhZmZmZlZjhNkMzMzM7McJ8gHu77sABLHMaQRYgDHkdcIMYDjsObTjudKu+1zu+0vtOA+uw+ymZmZmVmOW5DNzMzMzHKcIJuZmZmZ5ThBzpG0XNImSZslXVHnbd0oqV9ST67saEl3SHo4/XtUKpek76S4/inptHGKYY6kOyVtkPSgpM+VFMcRku6V9I8Ux9WpfK6ke9L2filpYirvTNOb0+fd4xFHWvcESQ9IWlViDFsl/UvSekn3pbJCj0la93RJt0raKKlX0lklnBsnpe9hcHhW0udLiOML6dzskXRzOmcLPzesOdWqa1tZrXq9HVReR1pdtWtWK3CCnEiaAHwPuABYCFwqaWEdN3kTsLyi7ApgTUTMB9akaVJM89NwGfD9cYphH/DFiFgILAEuT/tcdBwvAcsi4hRgMbBc0hLgG8C1ETEPeBpYkeZfATydyq9N842XzwG9uekyYgA4JyIW594rWfQxAbgOuD0iFgCnkH0vhcYREZvS97AYOB14HvhNkXFImg18FjgjIhYBE4BLKO/csOZTq65tZbXq9XZQeR1pB5XXrOYXER6yBxXPAlbnpq8ErqzzNruBntz0JuD4NH48sCmN/xC4tNp84xzP74Bzy4wDmATcD7yJ7Fd5OiqPD7AaOCuNd6T5NA7b7iJLtpYBqwAVHUNa31bgmIqyQo8JMA34d+U+lXxunAf8veg4gNnANuDodKxXAeeXcW54aI1hsK4tO44C9/fler3sWArY11dcR8qOp6B9Puia1QqDW5CHDF4EB/WlsiLNiogn0viTwKw0XvfY0m3gU4F7yogj3ZJaD/QDdwBbgGciYl+Vbb0cR/p8NzBjHML4NvAl4ECanlFCDAAB/FHSOkmXpbKij8lcYAfwk3Sr8MeSJpcQR94lwM1pvLA4IuJx4JvAY8ATZMd6HeWcG9bkKurallZZr0dEy+8zB19H2kG1a1bTc4LcoCL7s6yQd/BJmgL8Gvh8RDxbRhwRsT+y2+hdwJnAgnpvM0/Su4D+iFhX5HZreEtEnEbWXeBySW/Nf1jQMekATgO+HxGnAnsY6sZQZBwApP69FwG/qvys3nGk/s0Xk/3R8GpgMgd3jzIb0XB1bSuqrNclLSo7pnpqsOtIkYa9ZjUrJ8hDHgfm5Ka7UlmRtks6HiD921/v2CQdTlZh/yIibisrjkER8QxwJ9kt6+mSOqps6+U40ufTgKf+z02fDVwkaStwC9ntsesKjgF4ucWSiOgn6297JsUfkz6gL9ficytZwlzWuXEBcH9EbE/TRcbxDuDfEbEjIgaA28jOl8LPDWteNeratpCr11v9D8uDriOSfl5uSPVX45rV9JwgD1kLzE9Ppk8ku527suAYVgIfSeMfIeunNlj+4fSE/hJgd+728phJEnAD0BsR3yoxjpmSpqfxI8n6QfeSVajvqxHHYHzvA/6cWhHHLCKujIiuiOgmO/Z/jogPFBkDgKTJkqYOjpP1u+2h4GMSEU8C2ySdlIreDmwoOo6cSxnqXjG4vaLieAxYImlS+j8z+F0Uem5Y8xqmrm1ZNer1jeVGVV81riMfLDmsuhrmmtX8yu4E3UgDcCHwEFn/16/UeVs3k/VnHCBrrVtB1k9xDfAw8Cfg6DSvyN6wsQX4F9nT9OMRw1vIbk3/E1ifhgtLiOMNwAMpjh7ga6n8BOBeYDPZrfXOVH5Emt6cPj9hnI/NUtLDFUXHkLb3jzQ8OHgeFn1M0roXA/el4/Jb4KiS4phM1gI7LVdW9Dl6NdnFvQf4GdBZ1vnpofmGWnVt2XHVeZ+r1uvtMuSvI6081LpmtcLgn5o2MzMzM8txFwszMzMzsxwnyGZmZmZmOU6QzczMzMxynCCbmZmZmeU4QTYzMzMzy3GCbGZmZmaW4wTZzMzMzCzHCbJZjqRPSFqfhgO58Wtz83RLekHS+lzZc7nxCyU9JOk1adm9ko4pel/MzOz/I+kESTdIurXsWKxYTpDNciLixxGxGHgnsC0iFqfhCxWzbknzvYKktwPfAS6IiEfTPP+pf+RmZuWSdKOkfkk9FeXLJW2StFnSFSOVH8JnP5B01UiNGWneQ27QqLZPEfFIRKyoWOeRbvxofR1lB2DWoBaR/VTxIZP0VuBHZD8hu6UuUZmZNa6bgO8CPx0skDSB7OffzwX6gLWSVgKbqpVHxIZay0TEhrTaJcDpEXG1pNnAXdUaLHJGatA4H3iVpFUVs3w8Ivorl4uIF4DFkrYO/3VYM3OCbFbd64GeEeca0gn8FlgaERvrE5KZWeOKiL9K6q4oPhPYHBGPAEi6BbgY+EuN8g3DLLNB0uuAhyJif1r/qBsz0jqrNWi8a7TrsdblLhZm1Y220h0A7gJWjDSjmVkbmQ1sy033pbJa5cMtA3ABcHvus9E2ZsBQg8Z7RmrQkDRD0g+AUyVdOcrtWBNzgmxW3Wgr3QPA+4EzJX25PiGZmbW983llgjyWFuRDbtCIiKci4pMRcWJEfH2U27Em5gTZrIKkw4D5QO9olouI58ke7vuAJLckm5nB48Cc3HRXKqtVXnMZSZOA6RGRf/B5LC3IbtCwETlBNjvYPKAvIvaOdsGI2AUsB74q6aJxj8zMrLmsBeZLmitpInAJsHKY8uGWOQe4c3DFY23MADdo2Mj8kJ5ZhYh4CFg4ymWm5Ma3AXPHOy4zs0Ym6WZgKXCMpD7gqoi4QdKngdXABODGiHgwzV+1PCL2VftM0qeA/PuIx9yYkbazS9Jy4K+SdkTEyhEXsrahiCg7BrOmImkOWf+1p4Z7tZCkI4G7gZnA61PrspmZjYGk+4E3RcTAKJbpBlZFxKI6xLMVOCMido73uq18TpDNzMysJR1qg8Yo1+nGjzbgBNnMzMzMLMcP6ZmZmZmZ5ThBNjMzMzPLcYJsZmZmZpbjBNnMzMzMLMcJspmZmZlZjhNkMzMzM7McJ8hmZmZmZjlOkM3MzMzMcv4HR7C8tnBa/c0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from nonrad import get_C\n",
    "\n",
    "g = 4 # configurational degeneracy\n",
    "volume = ground_struct.volume # Angstrom^3\n",
    "\n",
    "# we pass in T, which is a numpy array\n",
    "# we will get the capture coefficient at each of these temperatures\n",
    "Ctilde = get_C(dQ, dE, excited_omega, ground_omega, Wif, volume, g=g, T=T)\n",
    "\n",
    "# apply Sommerfeld parameter, evaluated at the same temperatures\n",
    "C = f * Ctilde\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
    "ax[0].semilogy(T, C)\n",
    "ax[0].set_xlabel('$T$ [K]')\n",
    "ax[0].set_ylabel('$C_p$ [cm$^{3}$ s$^{-1}$]')\n",
    "ax[1].semilogy(1000 / T[200:], C[200:])\n",
    "ax[1].set_xlabel('$1000 / T$ [K$^{-1}$]')\n",
    "ax[1].set_ylabel('$C_p$ [cm$^{3}$ s$^{-1}$]')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We may also want to calculate the capture cross section, $\\sigma = C / \\langle v \\rangle$. We can do this using the `thermal_velocity` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from nonrad.scaling import thermal_velocity\n",
    "\n",
    "sigma = C / thermal_velocity(T, m_eff) # cm^2\n",
    "sigma *= (1e8)**2 # (cm to Angstrom)^2\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
    "ax[0].semilogy(T, sigma)\n",
    "ax[0].set_xlabel('$T$ [K]')\n",
    "ax[0].set_ylabel('$\\sigma$ [$\\AA^{2}$]')\n",
    "ax[1].semilogy(1000 / T[200:], sigma[200:])\n",
    "ax[1].set_xlabel('$1000 / T$ [K$^{-1}$]')\n",
    "ax[1].set_ylabel('$\\sigma$ [$\\AA^{2}$]')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "nonrad_py3",
   "language": "python",
   "name": "nonrad_py3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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